The latest round of sanctions is intended to tighten the screws on Russia by targeting broad sections of its economy and financial markets. So far, the U.S. and Europe Union have limited those targets to influential government officials — so-called phase two sanctions.

The new "phase three" sanctions target key specific sectors of Russia's economy from the defense industry to the banking sector. Those include an embargo on arms sales to Russia; a ban on exports of so-called dual-use goods such as computers or equipment that have both civilian and military uses; and efforts designed to cut off Russian banks from European capital markets.

The moves announced Tuesday further increase the risk that Russia raises the stakes in its widening economic and trade war with the West.

And both the European and Russian economies can ill afford any trade slowdown.

With an economy roughly the size of Italy's, Russia will feel the pain more intensely. Existing sanctions have all but wiped out growth in gross domestic product this year; the latest round is expected to throw the Russian economy sharply into reverse.

Europe's economy is barely moving ahead right now; GDP in the euro zone expanded just two-tenths of a percent in the latest three months, less than expected. Falling prices have stymied efforts to revive growth, so any loss of exports will hurt.

"An energy embargo, even for a short period of time, would plunge the already-weak Russian economy into a deep recession."

Still, even Europe's largest exporter, Germany, sent only 3.2 percent of its goods and services to Russia last year, accounting for just 1.2 percent of Germany's GDP, according to Capital Economics. Other euro zone countries may take a bigger hit to GDP, but the overall impact on growth could be relatively small.

Where Russia gets hit hardest

Among the sanctions announced Tuesday, the capital restrictions are expected to have the most damaging effect on Russia.

Last week, the Russian central bank raised interest rates from 7.5 percent to 8 percent — the third hike this year — to try to stem capital outflows and tamp down rising inflation. With Russian banks and private companies already suffering from capital flight, the restrictions on Western capital will squeeze them even harder.

That could force the government to step in and backstop banks and companies with heavy debt loads, according to economists at Capital Economics.

"If nothing else, the pickup in investment needed to revive Russia's ailing economy is starting to look ever more unlikely," they wrote in a note to clients.

Investors in Russia's financial markets are already feeling the pain. The Russian stock market is down by nearly 7 percent this month, and yields on five-year government bonds have jumped to more than 9.5 percent. If left in place for an extended period, the sanctions could cost investors in the Russian market as much as a trillion dollars, according to The Economist.

The loss of Russia as a borrower will also hurt European banks, especially those in the United Kingdom. It also raises the prospect that Moscow could retaliate by defaulting on outstanding loans. But Wells Fargo's chief global economist, Jay Bryson, estimates that the risk to Western bankers is fairly low.

Of the roughly $200 billion Russia owes U.S. and European banks, France has the largest exposure — with $47 billion in loans outstanding, or about 23 percent of its total foreign bank exposure. American banks hold $27 billion (13 percent of the total) worth of Russian debt, followed by Italy, Japan, Germany, the Netherlands and the U.K. Together, those seven countries account for 80 percent of the foreign bank exposure to Russia.

Energy risks for Russia

Much of the potential risk of wider sanctions has focused on Europe's dependence on Russian energy. But even there, Russia would likely come up on the losing end of any effort to cut off supplies.

Germany, for example, gets some 40 percent of its natural gas from Russia, but gas only makes up 20 percent of Germany's overall energy consumption, notes Julian Jessop, Capital Economics chief global economist. He figures that if Russia does turn off the gas, Germany could boost gas imports from other suppliers, through pipelines from Norway and the Netherlands, and draw on existing stocks. Other countries reliant on Russian gas, like Italy and Turkey, could increase imports from North Africa and the Middle East.

Russia would also sorely miss the revenue from energy sales, which account for about two-thirds of the country's exports — or about 20 percent of Russian GDP.

"An energy embargo, even for a short period of time, would plunge the already-weak Russian economy into a deep recession," said Bryson.

The ban on exports of dual-use equipment casts a wider net and could represent a larger loss of exports to Russia across the U.S. and Europe.

The impact of the embargo on arms sales and dual-use equipment is harder to predict.

France stood the most to lose from the arms embargo, thanks to a $1.2 billion order to deliver two warships to Russia. But the sanctions reportedly apply only to future deals. Russia has few other major outstanding defense contracts with the U.S. or other European nations.

The ban on exports of dual-use equipment casts a wider net, however, and could represent a larger loss of exports to Russia across the U.S. and Europe. But the sanctions leave it up to the seller to determine whether its products are going to end up being used by the Russian military.